1. Field of the Invention
The present invention relates to the determination of kinetic parameters for molecular interactions, and more particularly to a method for determining kinetic parameters for the interaction between a molecule immobilized to a solid support surface and a binding partner to the molecule in solution. The invention also relates to an analytical system, a computer program product and a computer system for performing the method.
2. Description of the Related Art
Analytical sensor systems that can monitor interactions between molecules, such as biomolecules, in real time are gaining increasing interest. These sensor systems, usually referred to as interaction analysis sensor systems or biospecific interaction analysis sensor systems, are often based on optical biosensors and affinity analysis and offer a rapid way to determine in real time inter alia equilibrium and rate constants without the need to label the interacting molecules. They have been used in the study of a variety of biomolecules, including proteins, nucleic acids, lipids and carbohydrates. In these systems, a sensor surface having one of the molecular reactants immobilized thereto is contacted with a solution containing the other reactant, either by providing a flow of the solution past the sensor surface, or in a cuvette or the like, and binding interactions at the surface are detected.
Conventionally, to determine, for example, association and dissociation rate constants (ka and kd, respectively) for the interaction between two interacting molecules, one of the molecules, often referred to as the ligand, is immobilized to a sensor surface and the other molecule, often referred to as the analyte, is provided in solution at several different known concentrations. Each concentration, or sample, of the analyte is then contacted with the sensor surface, either in a laminar flow past the sensor surface, or in a cuvette or the like, to permit association of the analyte to the sensor surface. After a sample has been brought to contact the sensor surface, the surface is contacted with a solution free from analyte, usually buffer, to permit dissociation of the analyte from the immobilized ligand. During these association and dissociation phases, the amount of binding of analyte to the surface is continuously detected and the binding data is collected. Before contacting the sensor surface with sample of a new analyte concentration, the ligand surface is restored or “regenerated” by treating the surface with a regeneration solution capable of removing any bound analyte while not destroying the ligand. In that way, all the different samples will contact essentially one and the same ligand surface as far as ligand density is concerned. The association and dissociation rate constants can then be obtained from the collected binding data by fitting the data to mathematical descriptions of interaction models in the form of differential equations. Usually, the binding data for all the samples are used in the same fit, a procedure referred to as global fitting. From the determined association and dissociation rate constants ka and kd, the equilibrium constant, KD, and the affinity constant KA (KA=1/KD) of the interaction can in turn be calculated. Alternatively, provided that the interaction reaches steady state during the association phase, the equilibrium constant can be directly obtained from the binding data without fitting.
Problems may arise, however, when the ligands are covalently immobilized to the sensor surface and suitable regeneration conditions are difficult to find. Renewed binding of the ligand via an immobilized capture agent before the contacting with each new analyte concentration could then be an alternative, but has the disadvantage of consuming large amounts of ligand for the determination.
Determination of equilibrium constants by a titration procedure without the requirement for regeneration of the immobilized ligands is described by Schuck, P., et al. (1998) Anal. Biochem. 265, 79-91. The sample is continuously circulated in a closed loop over two sensor spots of a commercial surface plasmon resonance biosensor. One of the sensor spots is functionalized with an immobilized ligand for a soluble analyte in the sample, and the other sensor spot serves as a reference surface. A binding isotherm for the interacting molecules is obtained by stepwise equilibrium titration of the analyte into the circulating loop, i.e., the sensor spots are sequentially contacted with stepwise increased concentrations of analyte until equilibrium is attained for each concentration. This equilibrium titration is said to be especially useful for the determination of binding constants in high-affinity systems since it eliminates the need for interpretation of binding kinetics and thereby problems that may arise from mass transport limitations.
A similar stepwise equilibrium titration procedure is described for a cuvette-based biosensor design in Hall, D. R., and Winzor, D. J. (1997) Anal. Biochem. 244, 152-160.
Also Myszka, D. G., et al. (1998) Anal. Biochem. 265, 326-330 discloses equilibrium analysis of high affinity interactions using a surface plasmon resonance-based biosensor. In this approach, the time available to collect association phase data is increased by placing the analyte directly into the running buffer. Complete equilibrium binding profiles were generated without a regeneration step by changing the concentration of analyte and allowing the surface reactions to reequilibrate. Analyte concentrations were also decreased to demonstrate that the binding reactions were fully reversible. In this way, equilibrium dissociation constants for very high affinity interactions could be determined.
Shank-Retzlaff, M. L., and Sligar, S. G. (2000) Anal. Chem. 72, 4212-4220 describes a one-step method for determining kinetic rates and equilibrium binding affinities by a technique called analyte-gradient surface plasmon resonance SPR (AG-SPR) which eliminates the need for surface regeneration. A gradient of analyte is passed over the sensor surface under continuous-flow conditions so that the concentration of analyte increases linearly with time. The rate at which analyte binds to immobilized ligands on the sensor surface is monitored by monitoring the change in the surface plasmon resonance as the analyte concentration increases. Kinetic rates are determined by fitting the data to a two-compartment model for the molecular interaction which permits use also for systems under mass transport limitations.
Titration procedures to determine binding capacity and regeneration conditions have been proposed by Karlsson, R., et al., Biasymposium 1998, Edinburgh 2-4 September 1998, 5th Biasymposium in Japan, Tokyo, Nov. 5-6, 1998.
US-A1-2003/0143565 discloses a method for determining interaction parameters, including rate constants, between an analyte and a ligand immobilized to a sensor surface, where a measurement can be performed several times in succession, e.g., in a cuvette, with a stepwise modification of the analyte concentration each time. The measurements need not be completed to equilibrium but can be interrupted earlier and the concentration of the analyte can be raised or lowered. Separate fitting of the binding curve part corresponding to each analyte concentration is used to determine respective initial binding rates, from which the association and dissociation rate constants for the interaction are then determined.
Thus, while titration procedures in combination with biosensors and affinity analysis are known per se in the art for determining equilibrium binding affinities, the use of multiple titrations to determine kinetic rate constants seems to be disclosed only in the above-mentioned publications Shank-Retzlaff, M. L., and Sligar, S. G. (2000), and US-A1-2003/0143565. The method according to Shank-Retzlaff, M. L., and Sligar, S. G. (2000) suffers from the limitation that it requires the use of a continuous gradient of the analyte. The method of US-A1-2003/0143565, on the other hand, is disadvantageous in that initial binding rates are frequently lower than the kinetic binding rate due to transport limitations, making initial binding rates unreliable for kinetic analysis. Further, this type of evaluation restricts the injection order of analyte concentrations.
From the prior art it may therefore be concluded that for determining kinetic rates for molecular interactions using systems based on biosensors and affinity analysis, it is necessary to regenerate the immobilized ligand prior to contacting the sensor surface with a different concentration of analyte to thereby present essentially one and the same ligand surface to each analyte concentration, unless (i) a continuous gradient of the analyte is used, or (ii) initial binding rates are determined in systems free from mass transport limitations.
It is an object of the present invention to provide a sensor-based method for determining chemical interaction parameters, including kinetic rate constants, by stepwise titration, which method obviates regeneration procedures while permitting measurements under mass transport limitation.